Integrand size = 545, antiderivative size = 37 \[ \int \frac {-16384 x^2-90112 x^3-236544 x^4-311808 x^5-108800 x^6+263744 x^7+404160 x^8+167680 x^9-15488 x^{10}+436 x^{11}-4 x^{12}+e^9 \left (-256 x^8+256 x^9\right )+e^6 \left (-3072 x^6-3584 x^7+384 x^8+7104 x^9-192 x^{10}\right )+e^3 \left (-12288 x^4-40960 x^5-57600 x^6-2944 x^7+70912 x^8+61856 x^9-3504 x^{10}+48 x^{11}\right )+\left (16384 x+81920 x^2+193536 x^3+163328 x^4-204544 x^5-671168 x^6-709472 x^7-241792 x^8+22976 x^9-652 x^{10}+6 x^{11}+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (3072 x^5+2048 x^6-4352 x^7-10560 x^8+288 x^9\right )+e^3 \left (12288 x^3+34816 x^4+30976 x^5-56960 x^6-141568 x^7-90816 x^8+5232 x^9-72 x^{10}\right )\right ) \log \left (x^2\right )+\left (8192 x+43008 x^2+148480 x^3+313344 x^4+407424 x^5+305312 x^6+74112 x^7+128 e^9 x^7-7488 x^8+216 x^9-2 x^{10}+e^6 \left (1536 x^5+3968 x^6+3456 x^7-96 x^8\right )+e^3 \left (6144 x^3+26624 x^4+59904 x^5+70656 x^6+28960 x^7-1728 x^8+24 x^9\right )\right ) \log ^2\left (x^2\right )}{4096+36864 x+138240 x^2+275712 x^3+306432 x^4+176256 x^5+36336 x^6+64 e^9 x^6-3744 x^7+108 x^8-x^9+e^6 \left (768 x^4+2304 x^5+1728 x^6-48 x^7\right )+e^3 \left (3072 x^2+18432 x^3+41472 x^4+41088 x^5+14400 x^6-864 x^7+12 x^8\right )} \, dx=\left (-\frac {5}{e^3+\left (3+\frac {2}{x}\right )^2-\frac {x}{4}}+x\right )^2 \left (-x+\log \left (x^2\right )\right )^2 \] Output:
(x-5/((3+2/x)^2-1/4*x+exp(3)))^2*(ln(x^2)-x)^2
Leaf count is larger than twice the leaf count of optimal. \(440\) vs. \(2(37)=74\).
Time = 0.25 (sec) , antiderivative size = 440, normalized size of antiderivative = 11.89 \[ \int \frac {-16384 x^2-90112 x^3-236544 x^4-311808 x^5-108800 x^6+263744 x^7+404160 x^8+167680 x^9-15488 x^{10}+436 x^{11}-4 x^{12}+e^9 \left (-256 x^8+256 x^9\right )+e^6 \left (-3072 x^6-3584 x^7+384 x^8+7104 x^9-192 x^{10}\right )+e^3 \left (-12288 x^4-40960 x^5-57600 x^6-2944 x^7+70912 x^8+61856 x^9-3504 x^{10}+48 x^{11}\right )+\left (16384 x+81920 x^2+193536 x^3+163328 x^4-204544 x^5-671168 x^6-709472 x^7-241792 x^8+22976 x^9-652 x^{10}+6 x^{11}+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (3072 x^5+2048 x^6-4352 x^7-10560 x^8+288 x^9\right )+e^3 \left (12288 x^3+34816 x^4+30976 x^5-56960 x^6-141568 x^7-90816 x^8+5232 x^9-72 x^{10}\right )\right ) \log \left (x^2\right )+\left (8192 x+43008 x^2+148480 x^3+313344 x^4+407424 x^5+305312 x^6+74112 x^7+128 e^9 x^7-7488 x^8+216 x^9-2 x^{10}+e^6 \left (1536 x^5+3968 x^6+3456 x^7-96 x^8\right )+e^3 \left (6144 x^3+26624 x^4+59904 x^5+70656 x^6+28960 x^7-1728 x^8+24 x^9\right )\right ) \log ^2\left (x^2\right )}{4096+36864 x+138240 x^2+275712 x^3+306432 x^4+176256 x^5+36336 x^6+64 e^9 x^6-3744 x^7+108 x^8-x^9+e^6 \left (768 x^4+2304 x^5+1728 x^6-48 x^7\right )+e^3 \left (3072 x^2+18432 x^3+41472 x^4+41088 x^5+14400 x^6-864 x^7+12 x^8\right )} \, dx=-\frac {13864960+2949120 e^3+163840 e^6+83189760 x+17694720 e^3 x+983040 e^6 x+187176960 x^2+46745600 e^3 x^2+3686400 e^6 x^2+81920 e^9 x^2+185443840 x^3+60241920 e^3 x^3+6615040 e^6 x^3+245760 e^9 x^3+64991744 x^4+29422080 e^3 x^4+4952320 e^6 x^4+368640 e^9 x^4+10240 e^{12} x^4-3900416 x^5-1262720 e^3 x^5-138240 e^6 x^5-5120 e^9 x^5+52224 x^6+11392 e^3 x^6+640 e^6 x^6-1984 x^7-224 e^3 x^7-1240 x^8-288 e^3 x^8-16 e^6 x^8+72 x^9+8 e^3 x^9-x^{10}+640 \left (9+e^3\right ) \left (16+48 x+4 \left (9+e^3\right ) x^2-x^3\right )^2 \log (x)-2 \left (368640+2211840 x+4976640 x^2+4930304 x^3+1727104 x^4+2560 e^9 x^4-105616 x^5-544 x^6-1240 x^7+72 x^8-x^9-16 e^6 x^2 \left (-1280-3840 x-4320 x^2+80 x^3+x^5\right )+8 e^3 \left (5120+30720 x+92160 x^2+137600 x^3+75840 x^4-2896 x^5-8 x^6-36 x^7+x^8\right )\right ) \log \left (x^2\right )-x^2 \left (16+28 x+4 \left (9+e^3\right ) x^2-x^3\right )^2 \log ^2\left (x^2\right )}{\left (16+48 x+4 \left (9+e^3\right ) x^2-x^3\right )^2} \] Input:
Integrate[(-16384*x^2 - 90112*x^3 - 236544*x^4 - 311808*x^5 - 108800*x^6 + 263744*x^7 + 404160*x^8 + 167680*x^9 - 15488*x^10 + 436*x^11 - 4*x^12 + E ^9*(-256*x^8 + 256*x^9) + E^6*(-3072*x^6 - 3584*x^7 + 384*x^8 + 7104*x^9 - 192*x^10) + E^3*(-12288*x^4 - 40960*x^5 - 57600*x^6 - 2944*x^7 + 70912*x^ 8 + 61856*x^9 - 3504*x^10 + 48*x^11) + (16384*x + 81920*x^2 + 193536*x^3 + 163328*x^4 - 204544*x^5 - 671168*x^6 - 709472*x^7 - 241792*x^8 + 22976*x^ 9 - 652*x^10 + 6*x^11 + E^9*(256*x^7 - 384*x^8) + E^6*(3072*x^5 + 2048*x^6 - 4352*x^7 - 10560*x^8 + 288*x^9) + E^3*(12288*x^3 + 34816*x^4 + 30976*x^ 5 - 56960*x^6 - 141568*x^7 - 90816*x^8 + 5232*x^9 - 72*x^10))*Log[x^2] + ( 8192*x + 43008*x^2 + 148480*x^3 + 313344*x^4 + 407424*x^5 + 305312*x^6 + 7 4112*x^7 + 128*E^9*x^7 - 7488*x^8 + 216*x^9 - 2*x^10 + E^6*(1536*x^5 + 396 8*x^6 + 3456*x^7 - 96*x^8) + E^3*(6144*x^3 + 26624*x^4 + 59904*x^5 + 70656 *x^6 + 28960*x^7 - 1728*x^8 + 24*x^9))*Log[x^2]^2)/(4096 + 36864*x + 13824 0*x^2 + 275712*x^3 + 306432*x^4 + 176256*x^5 + 36336*x^6 + 64*E^9*x^6 - 37 44*x^7 + 108*x^8 - x^9 + E^6*(768*x^4 + 2304*x^5 + 1728*x^6 - 48*x^7) + E^ 3*(3072*x^2 + 18432*x^3 + 41472*x^4 + 41088*x^5 + 14400*x^6 - 864*x^7 + 12 *x^8)),x]
Output:
-((13864960 + 2949120*E^3 + 163840*E^6 + 83189760*x + 17694720*E^3*x + 983 040*E^6*x + 187176960*x^2 + 46745600*E^3*x^2 + 3686400*E^6*x^2 + 81920*E^9 *x^2 + 185443840*x^3 + 60241920*E^3*x^3 + 6615040*E^6*x^3 + 245760*E^9*x^3 + 64991744*x^4 + 29422080*E^3*x^4 + 4952320*E^6*x^4 + 368640*E^9*x^4 + 10 240*E^12*x^4 - 3900416*x^5 - 1262720*E^3*x^5 - 138240*E^6*x^5 - 5120*E^9*x ^5 + 52224*x^6 + 11392*E^3*x^6 + 640*E^6*x^6 - 1984*x^7 - 224*E^3*x^7 - 12 40*x^8 - 288*E^3*x^8 - 16*E^6*x^8 + 72*x^9 + 8*E^3*x^9 - x^10 + 640*(9 + E ^3)*(16 + 48*x + 4*(9 + E^3)*x^2 - x^3)^2*Log[x] - 2*(368640 + 2211840*x + 4976640*x^2 + 4930304*x^3 + 1727104*x^4 + 2560*E^9*x^4 - 105616*x^5 - 544 *x^6 - 1240*x^7 + 72*x^8 - x^9 - 16*E^6*x^2*(-1280 - 3840*x - 4320*x^2 + 8 0*x^3 + x^5) + 8*E^3*(5120 + 30720*x + 92160*x^2 + 137600*x^3 + 75840*x^4 - 2896*x^5 - 8*x^6 - 36*x^7 + x^8))*Log[x^2] - x^2*(16 + 28*x + 4*(9 + E^3 )*x^2 - x^3)^2*Log[x^2]^2)/(16 + 48*x + 4*(9 + E^3)*x^2 - x^3)^2)
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-4 x^{12}+436 x^{11}-15488 x^{10}+167680 x^9+404160 x^8+263744 x^7-108800 x^6-311808 x^5-236544 x^4-90112 x^3-16384 x^2+e^9 \left (256 x^9-256 x^8\right )+e^6 \left (-192 x^{10}+7104 x^9+384 x^8-3584 x^7-3072 x^6\right )+e^3 \left (48 x^{11}-3504 x^{10}+61856 x^9+70912 x^8-2944 x^7-57600 x^6-40960 x^5-12288 x^4\right )+\left (-2 x^{10}+216 x^9-7488 x^8+128 e^9 x^7+74112 x^7+305312 x^6+407424 x^5+313344 x^4+148480 x^3+43008 x^2+e^6 \left (-96 x^8+3456 x^7+3968 x^6+1536 x^5\right )+e^3 \left (24 x^9-1728 x^8+28960 x^7+70656 x^6+59904 x^5+26624 x^4+6144 x^3\right )+8192 x\right ) \log ^2\left (x^2\right )+\left (6 x^{11}-652 x^{10}+22976 x^9-241792 x^8-709472 x^7-671168 x^6-204544 x^5+163328 x^4+193536 x^3+81920 x^2+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (288 x^9-10560 x^8-4352 x^7+2048 x^6+3072 x^5\right )+e^3 \left (-72 x^{10}+5232 x^9-90816 x^8-141568 x^7-56960 x^6+30976 x^5+34816 x^4+12288 x^3\right )+16384 x\right ) \log \left (x^2\right )}{-x^9+108 x^8-3744 x^7+64 e^9 x^6+36336 x^6+176256 x^5+306432 x^4+275712 x^3+138240 x^2+e^6 \left (-48 x^7+1728 x^6+2304 x^5+768 x^4\right )+e^3 \left (12 x^8-864 x^7+14400 x^6+41088 x^5+41472 x^4+18432 x^3+3072 x^2\right )+36864 x+4096} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-4 x^{12}+436 x^{11}-15488 x^{10}+167680 x^9+404160 x^8+263744 x^7-108800 x^6-311808 x^5-236544 x^4-90112 x^3-16384 x^2+e^9 \left (256 x^9-256 x^8\right )+e^6 \left (-192 x^{10}+7104 x^9+384 x^8-3584 x^7-3072 x^6\right )+e^3 \left (48 x^{11}-3504 x^{10}+61856 x^9+70912 x^8-2944 x^7-57600 x^6-40960 x^5-12288 x^4\right )+\left (-2 x^{10}+216 x^9-7488 x^8+128 e^9 x^7+74112 x^7+305312 x^6+407424 x^5+313344 x^4+148480 x^3+43008 x^2+e^6 \left (-96 x^8+3456 x^7+3968 x^6+1536 x^5\right )+e^3 \left (24 x^9-1728 x^8+28960 x^7+70656 x^6+59904 x^5+26624 x^4+6144 x^3\right )+8192 x\right ) \log ^2\left (x^2\right )+\left (6 x^{11}-652 x^{10}+22976 x^9-241792 x^8-709472 x^7-671168 x^6-204544 x^5+163328 x^4+193536 x^3+81920 x^2+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (288 x^9-10560 x^8-4352 x^7+2048 x^6+3072 x^5\right )+e^3 \left (-72 x^{10}+5232 x^9-90816 x^8-141568 x^7-56960 x^6+30976 x^5+34816 x^4+12288 x^3\right )+16384 x\right ) \log \left (x^2\right )}{-x^9+108 x^8-3744 x^7+\left (36336+64 e^9\right ) x^6+176256 x^5+306432 x^4+275712 x^3+138240 x^2+e^6 \left (-48 x^7+1728 x^6+2304 x^5+768 x^4\right )+e^3 \left (12 x^8-864 x^7+14400 x^6+41088 x^5+41472 x^4+18432 x^3+3072 x^2\right )+36864 x+4096}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int -\frac {-4 x^{12}+436 x^{11}-15488 x^{10}+167680 x^9+404160 x^8+263744 x^7-108800 x^6-311808 x^5-236544 x^4-90112 x^3-16384 x^2+e^9 \left (256 x^9-256 x^8\right )+e^6 \left (-192 x^{10}+7104 x^9+384 x^8-3584 x^7-3072 x^6\right )+e^3 \left (48 x^{11}-3504 x^{10}+61856 x^9+70912 x^8-2944 x^7-57600 x^6-40960 x^5-12288 x^4\right )+\left (-2 x^{10}+216 x^9-7488 x^8+128 e^9 x^7+74112 x^7+305312 x^6+407424 x^5+313344 x^4+148480 x^3+43008 x^2+e^6 \left (-96 x^8+3456 x^7+3968 x^6+1536 x^5\right )+e^3 \left (24 x^9-1728 x^8+28960 x^7+70656 x^6+59904 x^5+26624 x^4+6144 x^3\right )+8192 x\right ) \log ^2\left (x^2\right )+\left (6 x^{11}-652 x^{10}+22976 x^9-241792 x^8-709472 x^7-671168 x^6-204544 x^5+163328 x^4+193536 x^3+81920 x^2+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (288 x^9-10560 x^8-4352 x^7+2048 x^6+3072 x^5\right )+e^3 \left (-72 x^{10}+5232 x^9-90816 x^8-141568 x^7-56960 x^6+30976 x^5+34816 x^4+12288 x^3\right )+16384 x\right ) \log \left (x^2\right )}{\left (x^3-4 e^3 x^2-36 x^2-48 x-16\right )^3}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {4 x^{12}-436 x^{11}+15488 x^{10}-167680 x^9-404160 x^8-263744 x^7+108800 x^6+311808 x^5+236544 x^4+90112 x^3+16384 x^2-e^9 \left (256 x^9-256 x^8\right )-e^6 \left (-192 x^{10}+7104 x^9+384 x^8-3584 x^7-3072 x^6\right )-e^3 \left (48 x^{11}-3504 x^{10}+61856 x^9+70912 x^8-2944 x^7-57600 x^6-40960 x^5-12288 x^4\right )-\left (-2 x^{10}+216 x^9-7488 x^8+128 e^9 x^7+74112 x^7+305312 x^6+407424 x^5+313344 x^4+148480 x^3+43008 x^2+e^6 \left (-96 x^8+3456 x^7+3968 x^6+1536 x^5\right )+e^3 \left (24 x^9-1728 x^8+28960 x^7+70656 x^6+59904 x^5+26624 x^4+6144 x^3\right )+8192 x\right ) \log ^2\left (x^2\right )-\left (6 x^{11}-652 x^{10}+22976 x^9-241792 x^8-709472 x^7-671168 x^6-204544 x^5+163328 x^4+193536 x^3+81920 x^2+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (288 x^9-10560 x^8-4352 x^7+2048 x^6+3072 x^5\right )+e^3 \left (-72 x^{10}+5232 x^9-90816 x^8-141568 x^7-56960 x^6+30976 x^5+34816 x^4+12288 x^3\right )+16384 x\right ) \log \left (x^2\right )}{\left (x^3+\left (-36-4 e^3\right ) x^2-48 x-16\right )^3}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )-\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (2 \left (-x^7+\left (73+8 e^3\right ) x^6-8 \left (159+37 e^3+2 e^6\right ) x^5-4 \left (461+14 e^3-4 e^6\right ) x^4+16 \left (13+11 e^3\right ) x^3+32 \left (45+4 e^3\right ) x^2+960 x+256\right )+\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (2 \left (-x^7+\left (73+8 e^3\right ) x^6-8 \left (159+37 e^3+2 e^6\right ) x^5-4 \left (461+14 e^3-4 e^6\right ) x^4+16 \left (13+11 e^3\right ) x^3+32 \left (45+4 e^3\right ) x^2+960 x+256\right )+\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {2 \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^7+73 \left (1+\frac {8 e^3}{73}\right ) x^6-1272 \left (1+\frac {1}{159} e^3 \left (37+2 e^3\right )\right ) x^5-1844 \left (1-\frac {2}{461} e^3 \left (-7+2 e^3\right )\right ) x^4+208 \left (1+\frac {11 e^3}{13}\right ) x^3+1440 \left (1+\frac {4 e^3}{45}\right ) x^2+960 x+256\right ) x^2}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (-x^6+72 \left (1+\frac {e^3}{9}\right ) x^5-1180 \left (1+\frac {4}{295} e^3 \left (18+e^3\right )\right ) x^4-3424 \left (1+\frac {12 e^3}{107}\right ) x^3-2496 \left (1+\frac {2 e^3}{39}\right ) x^2-896 x-256\right ) \log ^2\left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}+\frac {\left (-3 x^{10}+326 \left (1+\frac {18 e^3}{163}\right ) x^9-11488 \left (1+\frac {3 e^3 \left (109+6 e^3\right )}{1436}\right ) x^8+120896 \left (1+\frac {3 e^3 \left (473+55 e^3+2 e^6\right )}{3778}\right ) x^7+354736 \left (1-\frac {8 e^3 \left (-553-17 e^3+e^6\right )}{22171}\right ) x^6+335584 \left (1-\frac {2 e^3 \left (-445+16 e^3\right )}{10487}\right ) x^5+102272 \left (1-\frac {1}{799} e^3 \left (121+12 e^3\right )\right ) x^4-81664 \left (1+\frac {68 e^3}{319}\right ) x^3-96768 \left (1+\frac {4 e^3}{63}\right ) x^2-40960 x-8192\right ) \log \left (x^2\right ) x}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (-x^3+4 \left (9+e^3\right ) x^2+28 x+16\right ) \left (x-\log \left (x^2\right )\right ) \left (\left (x^6-8 \left (9+e^3\right ) x^5+4 \left (295+72 e^3+4 e^6\right ) x^4+32 \left (107+12 e^3\right ) x^3+64 \left (39+2 e^3\right ) x^2+896 x+256\right ) \log \left (x^2\right )-2 \left (x^7-\left (73+8 e^3\right ) x^6+8 \left (159+37 e^3+2 e^6\right ) x^5+\left (1844+56 e^3-16 e^6\right ) x^4-16 \left (13+11 e^3\right ) x^3-32 \left (45+4 e^3\right ) x^2-960 x-256\right )\right )}{\left (-x^3+4 \left (9+e^3\right ) x^2+48 x+16\right )^3}dx\) |
Input:
Int[(-16384*x^2 - 90112*x^3 - 236544*x^4 - 311808*x^5 - 108800*x^6 + 26374 4*x^7 + 404160*x^8 + 167680*x^9 - 15488*x^10 + 436*x^11 - 4*x^12 + E^9*(-2 56*x^8 + 256*x^9) + E^6*(-3072*x^6 - 3584*x^7 + 384*x^8 + 7104*x^9 - 192*x ^10) + E^3*(-12288*x^4 - 40960*x^5 - 57600*x^6 - 2944*x^7 + 70912*x^8 + 61 856*x^9 - 3504*x^10 + 48*x^11) + (16384*x + 81920*x^2 + 193536*x^3 + 16332 8*x^4 - 204544*x^5 - 671168*x^6 - 709472*x^7 - 241792*x^8 + 22976*x^9 - 65 2*x^10 + 6*x^11 + E^9*(256*x^7 - 384*x^8) + E^6*(3072*x^5 + 2048*x^6 - 435 2*x^7 - 10560*x^8 + 288*x^9) + E^3*(12288*x^3 + 34816*x^4 + 30976*x^5 - 56 960*x^6 - 141568*x^7 - 90816*x^8 + 5232*x^9 - 72*x^10))*Log[x^2] + (8192*x + 43008*x^2 + 148480*x^3 + 313344*x^4 + 407424*x^5 + 305312*x^6 + 74112*x ^7 + 128*E^9*x^7 - 7488*x^8 + 216*x^9 - 2*x^10 + E^6*(1536*x^5 + 3968*x^6 + 3456*x^7 - 96*x^8) + E^3*(6144*x^3 + 26624*x^4 + 59904*x^5 + 70656*x^6 + 28960*x^7 - 1728*x^8 + 24*x^9))*Log[x^2]^2)/(4096 + 36864*x + 138240*x^2 + 275712*x^3 + 306432*x^4 + 176256*x^5 + 36336*x^6 + 64*E^9*x^6 - 3744*x^7 + 108*x^8 - x^9 + E^6*(768*x^4 + 2304*x^5 + 1728*x^6 - 48*x^7) + E^3*(307 2*x^2 + 18432*x^3 + 41472*x^4 + 41088*x^5 + 14400*x^6 - 864*x^7 + 12*x^8)) ,x]
Output:
$Aborted
\[\int \frac {\left (128 x^{7} {\mathrm e}^{9}+\left (-96 x^{8}+3456 x^{7}+3968 x^{6}+1536 x^{5}\right ) {\mathrm e}^{6}+\left (24 x^{9}-1728 x^{8}+28960 x^{7}+70656 x^{6}+59904 x^{5}+26624 x^{4}+6144 x^{3}\right ) {\mathrm e}^{3}-2 x^{10}+216 x^{9}-7488 x^{8}+74112 x^{7}+305312 x^{6}+407424 x^{5}+313344 x^{4}+148480 x^{3}+43008 x^{2}+8192 x \right ) \ln \left (x^{2}\right )^{2}+\left (\left (-384 x^{8}+256 x^{7}\right ) {\mathrm e}^{9}+\left (288 x^{9}-10560 x^{8}-4352 x^{7}+2048 x^{6}+3072 x^{5}\right ) {\mathrm e}^{6}+\left (-72 x^{10}+5232 x^{9}-90816 x^{8}-141568 x^{7}-56960 x^{6}+30976 x^{5}+34816 x^{4}+12288 x^{3}\right ) {\mathrm e}^{3}+6 x^{11}-652 x^{10}+22976 x^{9}-241792 x^{8}-709472 x^{7}-671168 x^{6}-204544 x^{5}+163328 x^{4}+193536 x^{3}+81920 x^{2}+16384 x \right ) \ln \left (x^{2}\right )+\left (256 x^{9}-256 x^{8}\right ) {\mathrm e}^{9}+\left (-192 x^{10}+7104 x^{9}+384 x^{8}-3584 x^{7}-3072 x^{6}\right ) {\mathrm e}^{6}+\left (48 x^{11}-3504 x^{10}+61856 x^{9}+70912 x^{8}-2944 x^{7}-57600 x^{6}-40960 x^{5}-12288 x^{4}\right ) {\mathrm e}^{3}-4 x^{12}+436 x^{11}-15488 x^{10}+167680 x^{9}+404160 x^{8}+263744 x^{7}-108800 x^{6}-311808 x^{5}-236544 x^{4}-90112 x^{3}-16384 x^{2}}{64 x^{6} {\mathrm e}^{9}+\left (-48 x^{7}+1728 x^{6}+2304 x^{5}+768 x^{4}\right ) {\mathrm e}^{6}+\left (12 x^{8}-864 x^{7}+14400 x^{6}+41088 x^{5}+41472 x^{4}+18432 x^{3}+3072 x^{2}\right ) {\mathrm e}^{3}-x^{9}+108 x^{8}-3744 x^{7}+36336 x^{6}+176256 x^{5}+306432 x^{4}+275712 x^{3}+138240 x^{2}+36864 x +4096}d x\]
Input:
int(((128*x^7*exp(3)^3+(-96*x^8+3456*x^7+3968*x^6+1536*x^5)*exp(3)^2+(24*x ^9-1728*x^8+28960*x^7+70656*x^6+59904*x^5+26624*x^4+6144*x^3)*exp(3)-2*x^1 0+216*x^9-7488*x^8+74112*x^7+305312*x^6+407424*x^5+313344*x^4+148480*x^3+4 3008*x^2+8192*x)*ln(x^2)^2+((-384*x^8+256*x^7)*exp(3)^3+(288*x^9-10560*x^8 -4352*x^7+2048*x^6+3072*x^5)*exp(3)^2+(-72*x^10+5232*x^9-90816*x^8-141568* x^7-56960*x^6+30976*x^5+34816*x^4+12288*x^3)*exp(3)+6*x^11-652*x^10+22976* x^9-241792*x^8-709472*x^7-671168*x^6-204544*x^5+163328*x^4+193536*x^3+8192 0*x^2+16384*x)*ln(x^2)+(256*x^9-256*x^8)*exp(3)^3+(-192*x^10+7104*x^9+384* x^8-3584*x^7-3072*x^6)*exp(3)^2+(48*x^11-3504*x^10+61856*x^9+70912*x^8-294 4*x^7-57600*x^6-40960*x^5-12288*x^4)*exp(3)-4*x^12+436*x^11-15488*x^10+167 680*x^9+404160*x^8+263744*x^7-108800*x^6-311808*x^5-236544*x^4-90112*x^3-1 6384*x^2)/(64*x^6*exp(3)^3+(-48*x^7+1728*x^6+2304*x^5+768*x^4)*exp(3)^2+(1 2*x^8-864*x^7+14400*x^6+41088*x^5+41472*x^4+18432*x^3+3072*x^2)*exp(3)-x^9 +108*x^8-3744*x^7+36336*x^6+176256*x^5+306432*x^4+275712*x^3+138240*x^2+36 864*x+4096),x)
Output:
int(((128*x^7*exp(3)^3+(-96*x^8+3456*x^7+3968*x^6+1536*x^5)*exp(3)^2+(24*x ^9-1728*x^8+28960*x^7+70656*x^6+59904*x^5+26624*x^4+6144*x^3)*exp(3)-2*x^1 0+216*x^9-7488*x^8+74112*x^7+305312*x^6+407424*x^5+313344*x^4+148480*x^3+4 3008*x^2+8192*x)*ln(x^2)^2+((-384*x^8+256*x^7)*exp(3)^3+(288*x^9-10560*x^8 -4352*x^7+2048*x^6+3072*x^5)*exp(3)^2+(-72*x^10+5232*x^9-90816*x^8-141568* x^7-56960*x^6+30976*x^5+34816*x^4+12288*x^3)*exp(3)+6*x^11-652*x^10+22976* x^9-241792*x^8-709472*x^7-671168*x^6-204544*x^5+163328*x^4+193536*x^3+8192 0*x^2+16384*x)*ln(x^2)+(256*x^9-256*x^8)*exp(3)^3+(-192*x^10+7104*x^9+384* x^8-3584*x^7-3072*x^6)*exp(3)^2+(48*x^11-3504*x^10+61856*x^9+70912*x^8-294 4*x^7-57600*x^6-40960*x^5-12288*x^4)*exp(3)-4*x^12+436*x^11-15488*x^10+167 680*x^9+404160*x^8+263744*x^7-108800*x^6-311808*x^5-236544*x^4-90112*x^3-1 6384*x^2)/(64*x^6*exp(3)^3+(-48*x^7+1728*x^6+2304*x^5+768*x^4)*exp(3)^2+(1 2*x^8-864*x^7+14400*x^6+41088*x^5+41472*x^4+18432*x^3+3072*x^2)*exp(3)-x^9 +108*x^8-3744*x^7+36336*x^6+176256*x^5+306432*x^4+275712*x^3+138240*x^2+36 864*x+4096),x)
Leaf count of result is larger than twice the leaf count of optimal. 364 vs. \(2 (38) = 76\).
Time = 0.10 (sec) , antiderivative size = 364, normalized size of antiderivative = 9.84 \[ \int \frac {-16384 x^2-90112 x^3-236544 x^4-311808 x^5-108800 x^6+263744 x^7+404160 x^8+167680 x^9-15488 x^{10}+436 x^{11}-4 x^{12}+e^9 \left (-256 x^8+256 x^9\right )+e^6 \left (-3072 x^6-3584 x^7+384 x^8+7104 x^9-192 x^{10}\right )+e^3 \left (-12288 x^4-40960 x^5-57600 x^6-2944 x^7+70912 x^8+61856 x^9-3504 x^{10}+48 x^{11}\right )+\left (16384 x+81920 x^2+193536 x^3+163328 x^4-204544 x^5-671168 x^6-709472 x^7-241792 x^8+22976 x^9-652 x^{10}+6 x^{11}+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (3072 x^5+2048 x^6-4352 x^7-10560 x^8+288 x^9\right )+e^3 \left (12288 x^3+34816 x^4+30976 x^5-56960 x^6-141568 x^7-90816 x^8+5232 x^9-72 x^{10}\right )\right ) \log \left (x^2\right )+\left (8192 x+43008 x^2+148480 x^3+313344 x^4+407424 x^5+305312 x^6+74112 x^7+128 e^9 x^7-7488 x^8+216 x^9-2 x^{10}+e^6 \left (1536 x^5+3968 x^6+3456 x^7-96 x^8\right )+e^3 \left (6144 x^3+26624 x^4+59904 x^5+70656 x^6+28960 x^7-1728 x^8+24 x^9\right )\right ) \log ^2\left (x^2\right )}{4096+36864 x+138240 x^2+275712 x^3+306432 x^4+176256 x^5+36336 x^6+64 e^9 x^6-3744 x^7+108 x^8-x^9+e^6 \left (768 x^4+2304 x^5+1728 x^6-48 x^7\right )+e^3 \left (3072 x^2+18432 x^3+41472 x^4+41088 x^5+14400 x^6-864 x^7+12 x^8\right )} \, dx=\frac {x^{10} - 72 \, x^{9} + 1240 \, x^{8} + 1984 \, x^{7} - 52224 \, x^{6} + 3900416 \, x^{5} - 10240 \, x^{4} e^{12} - 64991744 \, x^{4} - 185443840 \, x^{3} + {\left (x^{8} - 72 \, x^{7} + 16 \, x^{6} e^{6} + 1240 \, x^{6} + 1984 \, x^{5} + 1936 \, x^{4} + 896 \, x^{3} + 256 \, x^{2} - 8 \, {\left (x^{7} - 36 \, x^{6} - 28 \, x^{5} - 16 \, x^{4}\right )} e^{3}\right )} \log \left (x^{2}\right )^{2} - 187176960 \, x^{2} + 5120 \, {\left (x^{5} - 72 \, x^{4} - 48 \, x^{3} - 16 \, x^{2}\right )} e^{9} + 16 \, {\left (x^{8} - 40 \, x^{6} + 8640 \, x^{5} - 309520 \, x^{4} - 413440 \, x^{3} - 230400 \, x^{2} - 61440 \, x - 10240\right )} e^{6} - 8 \, {\left (x^{9} - 36 \, x^{8} - 28 \, x^{7} + 1424 \, x^{6} - 157840 \, x^{5} + 3677760 \, x^{4} + 7530240 \, x^{3} + 5843200 \, x^{2} + 2211840 \, x + 368640\right )} e^{3} - 2 \, {\left (x^{9} - 72 \, x^{8} + 16 \, x^{7} e^{6} + 1240 \, x^{7} + 1984 \, x^{6} + 1936 \, x^{5} + 896 \, x^{4} + 256 \, x^{3} - 8 \, {\left (x^{8} - 36 \, x^{7} - 28 \, x^{6} - 16 \, x^{5}\right )} e^{3}\right )} \log \left (x^{2}\right ) - 83189760 \, x - 13864960}{x^{6} - 72 \, x^{5} + 16 \, x^{4} e^{6} + 1200 \, x^{4} + 3424 \, x^{3} + 3456 \, x^{2} - 8 \, {\left (x^{5} - 36 \, x^{4} - 48 \, x^{3} - 16 \, x^{2}\right )} e^{3} + 1536 \, x + 256} \] Input:
integrate(((128*x^7*exp(3)^3+(-96*x^8+3456*x^7+3968*x^6+1536*x^5)*exp(3)^2 +(24*x^9-1728*x^8+28960*x^7+70656*x^6+59904*x^5+26624*x^4+6144*x^3)*exp(3) -2*x^10+216*x^9-7488*x^8+74112*x^7+305312*x^6+407424*x^5+313344*x^4+148480 *x^3+43008*x^2+8192*x)*log(x^2)^2+((-384*x^8+256*x^7)*exp(3)^3+(288*x^9-10 560*x^8-4352*x^7+2048*x^6+3072*x^5)*exp(3)^2+(-72*x^10+5232*x^9-90816*x^8- 141568*x^7-56960*x^6+30976*x^5+34816*x^4+12288*x^3)*exp(3)+6*x^11-652*x^10 +22976*x^9-241792*x^8-709472*x^7-671168*x^6-204544*x^5+163328*x^4+193536*x ^3+81920*x^2+16384*x)*log(x^2)+(256*x^9-256*x^8)*exp(3)^3+(-192*x^10+7104* x^9+384*x^8-3584*x^7-3072*x^6)*exp(3)^2+(48*x^11-3504*x^10+61856*x^9+70912 *x^8-2944*x^7-57600*x^6-40960*x^5-12288*x^4)*exp(3)-4*x^12+436*x^11-15488* x^10+167680*x^9+404160*x^8+263744*x^7-108800*x^6-311808*x^5-236544*x^4-901 12*x^3-16384*x^2)/(64*x^6*exp(3)^3+(-48*x^7+1728*x^6+2304*x^5+768*x^4)*exp (3)^2+(12*x^8-864*x^7+14400*x^6+41088*x^5+41472*x^4+18432*x^3+3072*x^2)*ex p(3)-x^9+108*x^8-3744*x^7+36336*x^6+176256*x^5+306432*x^4+275712*x^3+13824 0*x^2+36864*x+4096),x, algorithm="fricas")
Output:
(x^10 - 72*x^9 + 1240*x^8 + 1984*x^7 - 52224*x^6 + 3900416*x^5 - 10240*x^4 *e^12 - 64991744*x^4 - 185443840*x^3 + (x^8 - 72*x^7 + 16*x^6*e^6 + 1240*x ^6 + 1984*x^5 + 1936*x^4 + 896*x^3 + 256*x^2 - 8*(x^7 - 36*x^6 - 28*x^5 - 16*x^4)*e^3)*log(x^2)^2 - 187176960*x^2 + 5120*(x^5 - 72*x^4 - 48*x^3 - 16 *x^2)*e^9 + 16*(x^8 - 40*x^6 + 8640*x^5 - 309520*x^4 - 413440*x^3 - 230400 *x^2 - 61440*x - 10240)*e^6 - 8*(x^9 - 36*x^8 - 28*x^7 + 1424*x^6 - 157840 *x^5 + 3677760*x^4 + 7530240*x^3 + 5843200*x^2 + 2211840*x + 368640)*e^3 - 2*(x^9 - 72*x^8 + 16*x^7*e^6 + 1240*x^7 + 1984*x^6 + 1936*x^5 + 896*x^4 + 256*x^3 - 8*(x^8 - 36*x^7 - 28*x^6 - 16*x^5)*e^3)*log(x^2) - 83189760*x - 13864960)/(x^6 - 72*x^5 + 16*x^4*e^6 + 1200*x^4 + 3424*x^3 + 3456*x^2 - 8 *(x^5 - 36*x^4 - 48*x^3 - 16*x^2)*e^3 + 1536*x + 256)
Leaf count of result is larger than twice the leaf count of optimal. 600 vs. \(2 (26) = 52\).
Time = 13.35 (sec) , antiderivative size = 600, normalized size of antiderivative = 16.22 \[ \int \frac {-16384 x^2-90112 x^3-236544 x^4-311808 x^5-108800 x^6+263744 x^7+404160 x^8+167680 x^9-15488 x^{10}+436 x^{11}-4 x^{12}+e^9 \left (-256 x^8+256 x^9\right )+e^6 \left (-3072 x^6-3584 x^7+384 x^8+7104 x^9-192 x^{10}\right )+e^3 \left (-12288 x^4-40960 x^5-57600 x^6-2944 x^7+70912 x^8+61856 x^9-3504 x^{10}+48 x^{11}\right )+\left (16384 x+81920 x^2+193536 x^3+163328 x^4-204544 x^5-671168 x^6-709472 x^7-241792 x^8+22976 x^9-652 x^{10}+6 x^{11}+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (3072 x^5+2048 x^6-4352 x^7-10560 x^8+288 x^9\right )+e^3 \left (12288 x^3+34816 x^4+30976 x^5-56960 x^6-141568 x^7-90816 x^8+5232 x^9-72 x^{10}\right )\right ) \log \left (x^2\right )+\left (8192 x+43008 x^2+148480 x^3+313344 x^4+407424 x^5+305312 x^6+74112 x^7+128 e^9 x^7-7488 x^8+216 x^9-2 x^{10}+e^6 \left (1536 x^5+3968 x^6+3456 x^7-96 x^8\right )+e^3 \left (6144 x^3+26624 x^4+59904 x^5+70656 x^6+28960 x^7-1728 x^8+24 x^9\right )\right ) \log ^2\left (x^2\right )}{4096+36864 x+138240 x^2+275712 x^3+306432 x^4+176256 x^5+36336 x^6+64 e^9 x^6-3744 x^7+108 x^8-x^9+e^6 \left (768 x^4+2304 x^5+1728 x^6-48 x^7\right )+e^3 \left (3072 x^2+18432 x^3+41472 x^4+41088 x^5+14400 x^6-864 x^7+12 x^8\right )} \, dx=x^{4} + 40 x^{2} + x \left (1440 + 160 e^{3}\right ) - 640 \cdot \left (9 + e^{3}\right ) \log {\left (x \right )} + \frac {\left (x^{8} - 8 x^{7} e^{3} - 72 x^{7} + 1240 x^{6} + 288 x^{6} e^{3} + 16 x^{6} e^{6} + 1984 x^{5} + 224 x^{5} e^{3} + 1936 x^{4} + 128 x^{4} e^{3} + 896 x^{3} + 256 x^{2}\right ) \log {\left (x^{2} \right )}^{2}}{x^{6} - 8 x^{5} e^{3} - 72 x^{5} + 1200 x^{4} + 288 x^{4} e^{3} + 16 x^{4} e^{6} + 3424 x^{3} + 384 x^{3} e^{3} + 128 x^{2} e^{3} + 3456 x^{2} + 1536 x + 256} + \frac {\left (- 2 x^{9} + 144 x^{8} + 16 x^{8} e^{3} - 32 x^{7} e^{6} - 576 x^{7} e^{3} - 2480 x^{7} - 128 x^{6} e^{3} - 1088 x^{6} - 2560 x^{5} e^{6} - 46336 x^{5} e^{3} - 211232 x^{5} + 3454208 x^{4} + 1213440 x^{4} e^{3} + 5120 x^{4} e^{9} + 138240 x^{4} e^{6} + 9860608 x^{3} + 2201600 x^{3} e^{3} + 122880 x^{3} e^{6} + 9953280 x^{2} + 40960 x^{2} e^{6} + 1474560 x^{2} e^{3} + 4423680 x + 491520 x e^{3} + 737280 + 81920 e^{3}\right ) \log {\left (x^{2} \right )}}{x^{6} - 8 x^{5} e^{3} - 72 x^{5} + 1200 x^{4} + 288 x^{4} e^{3} + 16 x^{4} e^{6} + 3424 x^{3} + 384 x^{3} e^{3} + 128 x^{2} e^{3} + 3456 x^{2} + 1536 x + 256} + \frac {x^{5} \cdot \left (2033920 + 640640 e^{3} + 2560 e^{9} + 69120 e^{6}\right ) + x^{4} \left (- 368640 e^{9} - 5013760 e^{6} - 10240 e^{12} - 30528000 e^{3} - 70060800\right ) + x^{3} \left (- 6635520 e^{6} - 245760 e^{9} - 60979200 e^{3} - 190481920\right ) + x^{2} \left (- 3686400 e^{6} - 46991360 e^{3} - 81920 e^{9} - 189399040\right ) + x \left (- 983040 e^{6} - 17735680 e^{3} - 83558400\right ) - 163840 e^{6} - 2949120 e^{3} - 13864960}{x^{6} + x^{5} \left (- 8 e^{3} - 72\right ) + x^{4} \cdot \left (1200 + 288 e^{3} + 16 e^{6}\right ) + x^{3} \cdot \left (3424 + 384 e^{3}\right ) + x^{2} \cdot \left (128 e^{3} + 3456\right ) + 1536 x + 256} \] Input:
integrate(((128*x**7*exp(3)**3+(-96*x**8+3456*x**7+3968*x**6+1536*x**5)*ex p(3)**2+(24*x**9-1728*x**8+28960*x**7+70656*x**6+59904*x**5+26624*x**4+614 4*x**3)*exp(3)-2*x**10+216*x**9-7488*x**8+74112*x**7+305312*x**6+407424*x* *5+313344*x**4+148480*x**3+43008*x**2+8192*x)*ln(x**2)**2+((-384*x**8+256* x**7)*exp(3)**3+(288*x**9-10560*x**8-4352*x**7+2048*x**6+3072*x**5)*exp(3) **2+(-72*x**10+5232*x**9-90816*x**8-141568*x**7-56960*x**6+30976*x**5+3481 6*x**4+12288*x**3)*exp(3)+6*x**11-652*x**10+22976*x**9-241792*x**8-709472* x**7-671168*x**6-204544*x**5+163328*x**4+193536*x**3+81920*x**2+16384*x)*l n(x**2)+(256*x**9-256*x**8)*exp(3)**3+(-192*x**10+7104*x**9+384*x**8-3584* x**7-3072*x**6)*exp(3)**2+(48*x**11-3504*x**10+61856*x**9+70912*x**8-2944* x**7-57600*x**6-40960*x**5-12288*x**4)*exp(3)-4*x**12+436*x**11-15488*x**1 0+167680*x**9+404160*x**8+263744*x**7-108800*x**6-311808*x**5-236544*x**4- 90112*x**3-16384*x**2)/(64*x**6*exp(3)**3+(-48*x**7+1728*x**6+2304*x**5+76 8*x**4)*exp(3)**2+(12*x**8-864*x**7+14400*x**6+41088*x**5+41472*x**4+18432 *x**3+3072*x**2)*exp(3)-x**9+108*x**8-3744*x**7+36336*x**6+176256*x**5+306 432*x**4+275712*x**3+138240*x**2+36864*x+4096),x)
Output:
x**4 + 40*x**2 + x*(1440 + 160*exp(3)) - 640*(9 + exp(3))*log(x) + (x**8 - 8*x**7*exp(3) - 72*x**7 + 1240*x**6 + 288*x**6*exp(3) + 16*x**6*exp(6) + 1984*x**5 + 224*x**5*exp(3) + 1936*x**4 + 128*x**4*exp(3) + 896*x**3 + 256 *x**2)*log(x**2)**2/(x**6 - 8*x**5*exp(3) - 72*x**5 + 1200*x**4 + 288*x**4 *exp(3) + 16*x**4*exp(6) + 3424*x**3 + 384*x**3*exp(3) + 128*x**2*exp(3) + 3456*x**2 + 1536*x + 256) + (-2*x**9 + 144*x**8 + 16*x**8*exp(3) - 32*x** 7*exp(6) - 576*x**7*exp(3) - 2480*x**7 - 128*x**6*exp(3) - 1088*x**6 - 256 0*x**5*exp(6) - 46336*x**5*exp(3) - 211232*x**5 + 3454208*x**4 + 1213440*x **4*exp(3) + 5120*x**4*exp(9) + 138240*x**4*exp(6) + 9860608*x**3 + 220160 0*x**3*exp(3) + 122880*x**3*exp(6) + 9953280*x**2 + 40960*x**2*exp(6) + 14 74560*x**2*exp(3) + 4423680*x + 491520*x*exp(3) + 737280 + 81920*exp(3))*l og(x**2)/(x**6 - 8*x**5*exp(3) - 72*x**5 + 1200*x**4 + 288*x**4*exp(3) + 1 6*x**4*exp(6) + 3424*x**3 + 384*x**3*exp(3) + 128*x**2*exp(3) + 3456*x**2 + 1536*x + 256) + (x**5*(2033920 + 640640*exp(3) + 2560*exp(9) + 69120*exp (6)) + x**4*(-368640*exp(9) - 5013760*exp(6) - 10240*exp(12) - 30528000*ex p(3) - 70060800) + x**3*(-6635520*exp(6) - 245760*exp(9) - 60979200*exp(3) - 190481920) + x**2*(-3686400*exp(6) - 46991360*exp(3) - 81920*exp(9) - 1 89399040) + x*(-983040*exp(6) - 17735680*exp(3) - 83558400) - 163840*exp(6 ) - 2949120*exp(3) - 13864960)/(x**6 + x**5*(-8*exp(3) - 72) + x**4*(1200 + 288*exp(3) + 16*exp(6)) + x**3*(3424 + 384*exp(3)) + x**2*(128*exp(3)...
Leaf count of result is larger than twice the leaf count of optimal. 339 vs. \(2 (38) = 76\).
Time = 0.12 (sec) , antiderivative size = 339, normalized size of antiderivative = 9.16 \[ \int \frac {-16384 x^2-90112 x^3-236544 x^4-311808 x^5-108800 x^6+263744 x^7+404160 x^8+167680 x^9-15488 x^{10}+436 x^{11}-4 x^{12}+e^9 \left (-256 x^8+256 x^9\right )+e^6 \left (-3072 x^6-3584 x^7+384 x^8+7104 x^9-192 x^{10}\right )+e^3 \left (-12288 x^4-40960 x^5-57600 x^6-2944 x^7+70912 x^8+61856 x^9-3504 x^{10}+48 x^{11}\right )+\left (16384 x+81920 x^2+193536 x^3+163328 x^4-204544 x^5-671168 x^6-709472 x^7-241792 x^8+22976 x^9-652 x^{10}+6 x^{11}+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (3072 x^5+2048 x^6-4352 x^7-10560 x^8+288 x^9\right )+e^3 \left (12288 x^3+34816 x^4+30976 x^5-56960 x^6-141568 x^7-90816 x^8+5232 x^9-72 x^{10}\right )\right ) \log \left (x^2\right )+\left (8192 x+43008 x^2+148480 x^3+313344 x^4+407424 x^5+305312 x^6+74112 x^7+128 e^9 x^7-7488 x^8+216 x^9-2 x^{10}+e^6 \left (1536 x^5+3968 x^6+3456 x^7-96 x^8\right )+e^3 \left (6144 x^3+26624 x^4+59904 x^5+70656 x^6+28960 x^7-1728 x^8+24 x^9\right )\right ) \log ^2\left (x^2\right )}{4096+36864 x+138240 x^2+275712 x^3+306432 x^4+176256 x^5+36336 x^6+64 e^9 x^6-3744 x^7+108 x^8-x^9+e^6 \left (768 x^4+2304 x^5+1728 x^6-48 x^7\right )+e^3 \left (3072 x^2+18432 x^3+41472 x^4+41088 x^5+14400 x^6-864 x^7+12 x^8\right )} \, dx=\frac {x^{10} - 8 \, x^{9} {\left (e^{3} + 9\right )} + 8 \, x^{8} {\left (2 \, e^{6} + 36 \, e^{3} + 155\right )} + 32 \, x^{7} {\left (7 \, e^{3} + 62\right )} - 128 \, x^{6} {\left (5 \, e^{6} + 89 \, e^{3} + 408\right )} + 128 \, x^{5} {\left (40 \, e^{9} + 1080 \, e^{6} + 9865 \, e^{3} + 30472\right )} - 256 \, x^{4} {\left (40 \, e^{12} + 1440 \, e^{9} + 19345 \, e^{6} + 114930 \, e^{3} + 253874\right )} - 2560 \, x^{3} {\left (96 \, e^{9} + 2584 \, e^{6} + 23532 \, e^{3} + 72439\right )} - 10240 \, x^{2} {\left (8 \, e^{9} + 360 \, e^{6} + 4565 \, e^{3} + 18279\right )} + 4 \, {\left (x^{8} - 8 \, x^{7} {\left (e^{3} + 9\right )} + 8 \, x^{6} {\left (2 \, e^{6} + 36 \, e^{3} + 155\right )} + 32 \, x^{5} {\left (7 \, e^{3} + 62\right )} + 16 \, x^{4} {\left (8 \, e^{3} + 121\right )} + 896 \, x^{3} + 256 \, x^{2}\right )} \log \left (x\right )^{2} - 122880 \, x {\left (8 \, e^{6} + 144 \, e^{3} + 677\right )} - 4 \, {\left (x^{9} - 8 \, x^{8} {\left (e^{3} + 9\right )} + 8 \, x^{7} {\left (2 \, e^{6} + 36 \, e^{3} + 155\right )} + 32 \, x^{6} {\left (7 \, e^{3} + 62\right )} + 16 \, x^{5} {\left (8 \, e^{3} + 121\right )} + 896 \, x^{4} + 256 \, x^{3}\right )} \log \left (x\right ) - 163840 \, e^{6} - 2949120 \, e^{3} - 13864960}{x^{6} - 8 \, x^{5} {\left (e^{3} + 9\right )} + 16 \, x^{4} {\left (e^{6} + 18 \, e^{3} + 75\right )} + 32 \, x^{3} {\left (12 \, e^{3} + 107\right )} + 128 \, x^{2} {\left (e^{3} + 27\right )} + 1536 \, x + 256} \] Input:
integrate(((128*x^7*exp(3)^3+(-96*x^8+3456*x^7+3968*x^6+1536*x^5)*exp(3)^2 +(24*x^9-1728*x^8+28960*x^7+70656*x^6+59904*x^5+26624*x^4+6144*x^3)*exp(3) -2*x^10+216*x^9-7488*x^8+74112*x^7+305312*x^6+407424*x^5+313344*x^4+148480 *x^3+43008*x^2+8192*x)*log(x^2)^2+((-384*x^8+256*x^7)*exp(3)^3+(288*x^9-10 560*x^8-4352*x^7+2048*x^6+3072*x^5)*exp(3)^2+(-72*x^10+5232*x^9-90816*x^8- 141568*x^7-56960*x^6+30976*x^5+34816*x^4+12288*x^3)*exp(3)+6*x^11-652*x^10 +22976*x^9-241792*x^8-709472*x^7-671168*x^6-204544*x^5+163328*x^4+193536*x ^3+81920*x^2+16384*x)*log(x^2)+(256*x^9-256*x^8)*exp(3)^3+(-192*x^10+7104* x^9+384*x^8-3584*x^7-3072*x^6)*exp(3)^2+(48*x^11-3504*x^10+61856*x^9+70912 *x^8-2944*x^7-57600*x^6-40960*x^5-12288*x^4)*exp(3)-4*x^12+436*x^11-15488* x^10+167680*x^9+404160*x^8+263744*x^7-108800*x^6-311808*x^5-236544*x^4-901 12*x^3-16384*x^2)/(64*x^6*exp(3)^3+(-48*x^7+1728*x^6+2304*x^5+768*x^4)*exp (3)^2+(12*x^8-864*x^7+14400*x^6+41088*x^5+41472*x^4+18432*x^3+3072*x^2)*ex p(3)-x^9+108*x^8-3744*x^7+36336*x^6+176256*x^5+306432*x^4+275712*x^3+13824 0*x^2+36864*x+4096),x, algorithm="maxima")
Output:
(x^10 - 8*x^9*(e^3 + 9) + 8*x^8*(2*e^6 + 36*e^3 + 155) + 32*x^7*(7*e^3 + 6 2) - 128*x^6*(5*e^6 + 89*e^3 + 408) + 128*x^5*(40*e^9 + 1080*e^6 + 9865*e^ 3 + 30472) - 256*x^4*(40*e^12 + 1440*e^9 + 19345*e^6 + 114930*e^3 + 253874 ) - 2560*x^3*(96*e^9 + 2584*e^6 + 23532*e^3 + 72439) - 10240*x^2*(8*e^9 + 360*e^6 + 4565*e^3 + 18279) + 4*(x^8 - 8*x^7*(e^3 + 9) + 8*x^6*(2*e^6 + 36 *e^3 + 155) + 32*x^5*(7*e^3 + 62) + 16*x^4*(8*e^3 + 121) + 896*x^3 + 256*x ^2)*log(x)^2 - 122880*x*(8*e^6 + 144*e^3 + 677) - 4*(x^9 - 8*x^8*(e^3 + 9) + 8*x^7*(2*e^6 + 36*e^3 + 155) + 32*x^6*(7*e^3 + 62) + 16*x^5*(8*e^3 + 12 1) + 896*x^4 + 256*x^3)*log(x) - 163840*e^6 - 2949120*e^3 - 13864960)/(x^6 - 8*x^5*(e^3 + 9) + 16*x^4*(e^6 + 18*e^3 + 75) + 32*x^3*(12*e^3 + 107) + 128*x^2*(e^3 + 27) + 1536*x + 256)
\[ \int \frac {-16384 x^2-90112 x^3-236544 x^4-311808 x^5-108800 x^6+263744 x^7+404160 x^8+167680 x^9-15488 x^{10}+436 x^{11}-4 x^{12}+e^9 \left (-256 x^8+256 x^9\right )+e^6 \left (-3072 x^6-3584 x^7+384 x^8+7104 x^9-192 x^{10}\right )+e^3 \left (-12288 x^4-40960 x^5-57600 x^6-2944 x^7+70912 x^8+61856 x^9-3504 x^{10}+48 x^{11}\right )+\left (16384 x+81920 x^2+193536 x^3+163328 x^4-204544 x^5-671168 x^6-709472 x^7-241792 x^8+22976 x^9-652 x^{10}+6 x^{11}+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (3072 x^5+2048 x^6-4352 x^7-10560 x^8+288 x^9\right )+e^3 \left (12288 x^3+34816 x^4+30976 x^5-56960 x^6-141568 x^7-90816 x^8+5232 x^9-72 x^{10}\right )\right ) \log \left (x^2\right )+\left (8192 x+43008 x^2+148480 x^3+313344 x^4+407424 x^5+305312 x^6+74112 x^7+128 e^9 x^7-7488 x^8+216 x^9-2 x^{10}+e^6 \left (1536 x^5+3968 x^6+3456 x^7-96 x^8\right )+e^3 \left (6144 x^3+26624 x^4+59904 x^5+70656 x^6+28960 x^7-1728 x^8+24 x^9\right )\right ) \log ^2\left (x^2\right )}{4096+36864 x+138240 x^2+275712 x^3+306432 x^4+176256 x^5+36336 x^6+64 e^9 x^6-3744 x^7+108 x^8-x^9+e^6 \left (768 x^4+2304 x^5+1728 x^6-48 x^7\right )+e^3 \left (3072 x^2+18432 x^3+41472 x^4+41088 x^5+14400 x^6-864 x^7+12 x^8\right )} \, dx=\int { \frac {2 \, {\left (2 \, x^{12} - 218 \, x^{11} + 7744 \, x^{10} - 83840 \, x^{9} - 202080 \, x^{8} - 131872 \, x^{7} + 54400 \, x^{6} + 155904 \, x^{5} + 118272 \, x^{4} + 45056 \, x^{3} + {\left (x^{10} - 108 \, x^{9} + 3744 \, x^{8} - 64 \, x^{7} e^{9} - 37056 \, x^{7} - 152656 \, x^{6} - 203712 \, x^{5} - 156672 \, x^{4} - 74240 \, x^{3} - 21504 \, x^{2} + 16 \, {\left (3 \, x^{8} - 108 \, x^{7} - 124 \, x^{6} - 48 \, x^{5}\right )} e^{6} - 4 \, {\left (3 \, x^{9} - 216 \, x^{8} + 3620 \, x^{7} + 8832 \, x^{6} + 7488 \, x^{5} + 3328 \, x^{4} + 768 \, x^{3}\right )} e^{3} - 4096 \, x\right )} \log \left (x^{2}\right )^{2} + 8192 \, x^{2} - 128 \, {\left (x^{9} - x^{8}\right )} e^{9} + 32 \, {\left (3 \, x^{10} - 111 \, x^{9} - 6 \, x^{8} + 56 \, x^{7} + 48 \, x^{6}\right )} e^{6} - 8 \, {\left (3 \, x^{11} - 219 \, x^{10} + 3866 \, x^{9} + 4432 \, x^{8} - 184 \, x^{7} - 3600 \, x^{6} - 2560 \, x^{5} - 768 \, x^{4}\right )} e^{3} - {\left (3 \, x^{11} - 326 \, x^{10} + 11488 \, x^{9} - 120896 \, x^{8} - 354736 \, x^{7} - 335584 \, x^{6} - 102272 \, x^{5} + 81664 \, x^{4} + 96768 \, x^{3} + 40960 \, x^{2} - 64 \, {\left (3 \, x^{8} - 2 \, x^{7}\right )} e^{9} + 16 \, {\left (9 \, x^{9} - 330 \, x^{8} - 136 \, x^{7} + 64 \, x^{6} + 96 \, x^{5}\right )} e^{6} - 4 \, {\left (9 \, x^{10} - 654 \, x^{9} + 11352 \, x^{8} + 17696 \, x^{7} + 7120 \, x^{6} - 3872 \, x^{5} - 4352 \, x^{4} - 1536 \, x^{3}\right )} e^{3} + 8192 \, x\right )} \log \left (x^{2}\right )\right )}}{x^{9} - 108 \, x^{8} + 3744 \, x^{7} - 64 \, x^{6} e^{9} - 36336 \, x^{6} - 176256 \, x^{5} - 306432 \, x^{4} - 275712 \, x^{3} - 138240 \, x^{2} + 48 \, {\left (x^{7} - 36 \, x^{6} - 48 \, x^{5} - 16 \, x^{4}\right )} e^{6} - 12 \, {\left (x^{8} - 72 \, x^{7} + 1200 \, x^{6} + 3424 \, x^{5} + 3456 \, x^{4} + 1536 \, x^{3} + 256 \, x^{2}\right )} e^{3} - 36864 \, x - 4096} \,d x } \] Input:
integrate(((128*x^7*exp(3)^3+(-96*x^8+3456*x^7+3968*x^6+1536*x^5)*exp(3)^2 +(24*x^9-1728*x^8+28960*x^7+70656*x^6+59904*x^5+26624*x^4+6144*x^3)*exp(3) -2*x^10+216*x^9-7488*x^8+74112*x^7+305312*x^6+407424*x^5+313344*x^4+148480 *x^3+43008*x^2+8192*x)*log(x^2)^2+((-384*x^8+256*x^7)*exp(3)^3+(288*x^9-10 560*x^8-4352*x^7+2048*x^6+3072*x^5)*exp(3)^2+(-72*x^10+5232*x^9-90816*x^8- 141568*x^7-56960*x^6+30976*x^5+34816*x^4+12288*x^3)*exp(3)+6*x^11-652*x^10 +22976*x^9-241792*x^8-709472*x^7-671168*x^6-204544*x^5+163328*x^4+193536*x ^3+81920*x^2+16384*x)*log(x^2)+(256*x^9-256*x^8)*exp(3)^3+(-192*x^10+7104* x^9+384*x^8-3584*x^7-3072*x^6)*exp(3)^2+(48*x^11-3504*x^10+61856*x^9+70912 *x^8-2944*x^7-57600*x^6-40960*x^5-12288*x^4)*exp(3)-4*x^12+436*x^11-15488* x^10+167680*x^9+404160*x^8+263744*x^7-108800*x^6-311808*x^5-236544*x^4-901 12*x^3-16384*x^2)/(64*x^6*exp(3)^3+(-48*x^7+1728*x^6+2304*x^5+768*x^4)*exp (3)^2+(12*x^8-864*x^7+14400*x^6+41088*x^5+41472*x^4+18432*x^3+3072*x^2)*ex p(3)-x^9+108*x^8-3744*x^7+36336*x^6+176256*x^5+306432*x^4+275712*x^3+13824 0*x^2+36864*x+4096),x, algorithm="giac")
Output:
integrate(2*(2*x^12 - 218*x^11 + 7744*x^10 - 83840*x^9 - 202080*x^8 - 1318 72*x^7 + 54400*x^6 + 155904*x^5 + 118272*x^4 + 45056*x^3 + (x^10 - 108*x^9 + 3744*x^8 - 64*x^7*e^9 - 37056*x^7 - 152656*x^6 - 203712*x^5 - 156672*x^ 4 - 74240*x^3 - 21504*x^2 + 16*(3*x^8 - 108*x^7 - 124*x^6 - 48*x^5)*e^6 - 4*(3*x^9 - 216*x^8 + 3620*x^7 + 8832*x^6 + 7488*x^5 + 3328*x^4 + 768*x^3)* e^3 - 4096*x)*log(x^2)^2 + 8192*x^2 - 128*(x^9 - x^8)*e^9 + 32*(3*x^10 - 1 11*x^9 - 6*x^8 + 56*x^7 + 48*x^6)*e^6 - 8*(3*x^11 - 219*x^10 + 3866*x^9 + 4432*x^8 - 184*x^7 - 3600*x^6 - 2560*x^5 - 768*x^4)*e^3 - (3*x^11 - 326*x^ 10 + 11488*x^9 - 120896*x^8 - 354736*x^7 - 335584*x^6 - 102272*x^5 + 81664 *x^4 + 96768*x^3 + 40960*x^2 - 64*(3*x^8 - 2*x^7)*e^9 + 16*(9*x^9 - 330*x^ 8 - 136*x^7 + 64*x^6 + 96*x^5)*e^6 - 4*(9*x^10 - 654*x^9 + 11352*x^8 + 176 96*x^7 + 7120*x^6 - 3872*x^5 - 4352*x^4 - 1536*x^3)*e^3 + 8192*x)*log(x^2) )/(x^9 - 108*x^8 + 3744*x^7 - 64*x^6*e^9 - 36336*x^6 - 176256*x^5 - 306432 *x^4 - 275712*x^3 - 138240*x^2 + 48*(x^7 - 36*x^6 - 48*x^5 - 16*x^4)*e^6 - 12*(x^8 - 72*x^7 + 1200*x^6 + 3424*x^5 + 3456*x^4 + 1536*x^3 + 256*x^2)*e ^3 - 36864*x - 4096), x)
Timed out. \[ \int \frac {-16384 x^2-90112 x^3-236544 x^4-311808 x^5-108800 x^6+263744 x^7+404160 x^8+167680 x^9-15488 x^{10}+436 x^{11}-4 x^{12}+e^9 \left (-256 x^8+256 x^9\right )+e^6 \left (-3072 x^6-3584 x^7+384 x^8+7104 x^9-192 x^{10}\right )+e^3 \left (-12288 x^4-40960 x^5-57600 x^6-2944 x^7+70912 x^8+61856 x^9-3504 x^{10}+48 x^{11}\right )+\left (16384 x+81920 x^2+193536 x^3+163328 x^4-204544 x^5-671168 x^6-709472 x^7-241792 x^8+22976 x^9-652 x^{10}+6 x^{11}+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (3072 x^5+2048 x^6-4352 x^7-10560 x^8+288 x^9\right )+e^3 \left (12288 x^3+34816 x^4+30976 x^5-56960 x^6-141568 x^7-90816 x^8+5232 x^9-72 x^{10}\right )\right ) \log \left (x^2\right )+\left (8192 x+43008 x^2+148480 x^3+313344 x^4+407424 x^5+305312 x^6+74112 x^7+128 e^9 x^7-7488 x^8+216 x^9-2 x^{10}+e^6 \left (1536 x^5+3968 x^6+3456 x^7-96 x^8\right )+e^3 \left (6144 x^3+26624 x^4+59904 x^5+70656 x^6+28960 x^7-1728 x^8+24 x^9\right )\right ) \log ^2\left (x^2\right )}{4096+36864 x+138240 x^2+275712 x^3+306432 x^4+176256 x^5+36336 x^6+64 e^9 x^6-3744 x^7+108 x^8-x^9+e^6 \left (768 x^4+2304 x^5+1728 x^6-48 x^7\right )+e^3 \left (3072 x^2+18432 x^3+41472 x^4+41088 x^5+14400 x^6-864 x^7+12 x^8\right )} \, dx=\text {Hanged} \] Input:
int(-(exp(6)*(3072*x^6 + 3584*x^7 - 384*x^8 - 7104*x^9 + 192*x^10) - log(x ^2)^2*(8192*x + 128*x^7*exp(9) + exp(3)*(6144*x^3 + 26624*x^4 + 59904*x^5 + 70656*x^6 + 28960*x^7 - 1728*x^8 + 24*x^9) + 43008*x^2 + 148480*x^3 + 31 3344*x^4 + 407424*x^5 + 305312*x^6 + 74112*x^7 - 7488*x^8 + 216*x^9 - 2*x^ 10 + exp(6)*(1536*x^5 + 3968*x^6 + 3456*x^7 - 96*x^8)) + exp(9)*(256*x^8 - 256*x^9) - log(x^2)*(16384*x + exp(6)*(3072*x^5 + 2048*x^6 - 4352*x^7 - 1 0560*x^8 + 288*x^9) + exp(9)*(256*x^7 - 384*x^8) + 81920*x^2 + 193536*x^3 + 163328*x^4 - 204544*x^5 - 671168*x^6 - 709472*x^7 - 241792*x^8 + 22976*x ^9 - 652*x^10 + 6*x^11 + exp(3)*(12288*x^3 + 34816*x^4 + 30976*x^5 - 56960 *x^6 - 141568*x^7 - 90816*x^8 + 5232*x^9 - 72*x^10)) + 16384*x^2 + 90112*x ^3 + 236544*x^4 + 311808*x^5 + 108800*x^6 - 263744*x^7 - 404160*x^8 - 1676 80*x^9 + 15488*x^10 - 436*x^11 + 4*x^12 + exp(3)*(12288*x^4 + 40960*x^5 + 57600*x^6 + 2944*x^7 - 70912*x^8 - 61856*x^9 + 3504*x^10 - 48*x^11))/(3686 4*x + 64*x^6*exp(9) + exp(3)*(3072*x^2 + 18432*x^3 + 41472*x^4 + 41088*x^5 + 14400*x^6 - 864*x^7 + 12*x^8) + 138240*x^2 + 275712*x^3 + 306432*x^4 + 176256*x^5 + 36336*x^6 - 3744*x^7 + 108*x^8 - x^9 + exp(6)*(768*x^4 + 2304 *x^5 + 1728*x^6 - 48*x^7) + 4096),x)
Output:
\text{Hanged}
Time = 0.32 (sec) , antiderivative size = 957, normalized size of antiderivative = 25.86 \[ \int \frac {-16384 x^2-90112 x^3-236544 x^4-311808 x^5-108800 x^6+263744 x^7+404160 x^8+167680 x^9-15488 x^{10}+436 x^{11}-4 x^{12}+e^9 \left (-256 x^8+256 x^9\right )+e^6 \left (-3072 x^6-3584 x^7+384 x^8+7104 x^9-192 x^{10}\right )+e^3 \left (-12288 x^4-40960 x^5-57600 x^6-2944 x^7+70912 x^8+61856 x^9-3504 x^{10}+48 x^{11}\right )+\left (16384 x+81920 x^2+193536 x^3+163328 x^4-204544 x^5-671168 x^6-709472 x^7-241792 x^8+22976 x^9-652 x^{10}+6 x^{11}+e^9 \left (256 x^7-384 x^8\right )+e^6 \left (3072 x^5+2048 x^6-4352 x^7-10560 x^8+288 x^9\right )+e^3 \left (12288 x^3+34816 x^4+30976 x^5-56960 x^6-141568 x^7-90816 x^8+5232 x^9-72 x^{10}\right )\right ) \log \left (x^2\right )+\left (8192 x+43008 x^2+148480 x^3+313344 x^4+407424 x^5+305312 x^6+74112 x^7+128 e^9 x^7-7488 x^8+216 x^9-2 x^{10}+e^6 \left (1536 x^5+3968 x^6+3456 x^7-96 x^8\right )+e^3 \left (6144 x^3+26624 x^4+59904 x^5+70656 x^6+28960 x^7-1728 x^8+24 x^9\right )\right ) \log ^2\left (x^2\right )}{4096+36864 x+138240 x^2+275712 x^3+306432 x^4+176256 x^5+36336 x^6+64 e^9 x^6-3744 x^7+108 x^8-x^9+e^6 \left (768 x^4+2304 x^5+1728 x^6-48 x^7\right )+e^3 \left (3072 x^2+18432 x^3+41472 x^4+41088 x^5+14400 x^6-864 x^7+12 x^8\right )} \, dx =\text {Too large to display} \] Input:
int(((128*x^7*exp(3)^3+(-96*x^8+3456*x^7+3968*x^6+1536*x^5)*exp(3)^2+(24*x ^9-1728*x^8+28960*x^7+70656*x^6+59904*x^5+26624*x^4+6144*x^3)*exp(3)-2*x^1 0+216*x^9-7488*x^8+74112*x^7+305312*x^6+407424*x^5+313344*x^4+148480*x^3+4 3008*x^2+8192*x)*log(x^2)^2+((-384*x^8+256*x^7)*exp(3)^3+(288*x^9-10560*x^ 8-4352*x^7+2048*x^6+3072*x^5)*exp(3)^2+(-72*x^10+5232*x^9-90816*x^8-141568 *x^7-56960*x^6+30976*x^5+34816*x^4+12288*x^3)*exp(3)+6*x^11-652*x^10+22976 *x^9-241792*x^8-709472*x^7-671168*x^6-204544*x^5+163328*x^4+193536*x^3+819 20*x^2+16384*x)*log(x^2)+(256*x^9-256*x^8)*exp(3)^3+(-192*x^10+7104*x^9+38 4*x^8-3584*x^7-3072*x^6)*exp(3)^2+(48*x^11-3504*x^10+61856*x^9+70912*x^8-2 944*x^7-57600*x^6-40960*x^5-12288*x^4)*exp(3)-4*x^12+436*x^11-15488*x^10+1 67680*x^9+404160*x^8+263744*x^7-108800*x^6-311808*x^5-236544*x^4-90112*x^3 -16384*x^2)/(64*x^6*exp(3)^3+(-48*x^7+1728*x^6+2304*x^5+768*x^4)*exp(3)^2+ (12*x^8-864*x^7+14400*x^6+41088*x^5+41472*x^4+18432*x^3+3072*x^2)*exp(3)-x ^9+108*x^8-3744*x^7+36336*x^6+176256*x^5+306432*x^4+275712*x^3+138240*x^2+ 36864*x+4096),x)
Output:
(16*log(x**2)**2*e**9*x**6 - 8*log(x**2)**2*e**6*x**7 + 432*log(x**2)**2*e **6*x**6 + 224*log(x**2)**2*e**6*x**5 + 128*log(x**2)**2*e**6*x**4 + log(x **2)**2*e**3*x**8 - 144*log(x**2)**2*e**3*x**7 + 3832*log(x**2)**2*e**3*x* *6 + 4000*log(x**2)**2*e**3*x**5 + 3088*log(x**2)**2*e**3*x**4 + 896*log(x **2)**2*e**3*x**3 + 256*log(x**2)**2*e**3*x**2 + 9*log(x**2)**2*x**8 - 648 *log(x**2)**2*x**7 + 11160*log(x**2)**2*x**6 + 17856*log(x**2)**2*x**5 + 1 7424*log(x**2)**2*x**4 + 8064*log(x**2)**2*x**3 + 2304*log(x**2)**2*x**2 - 32*log(x**2)*e**9*x**7 - 512*log(x**2)*e**9*x**4 + 16*log(x**2)*e**6*x**8 - 864*log(x**2)*e**6*x**7 - 448*log(x**2)*e**6*x**6 - 16960*log(x**2)*e** 6*x**4 - 12288*log(x**2)*e**6*x**3 - 4096*log(x**2)*e**6*x**2 - 2*log(x**2 )*e**3*x**9 + 288*log(x**2)*e**3*x**8 - 7664*log(x**2)*e**3*x**7 - 8032*lo g(x**2)*e**3*x**6 - 179584*log(x**2)*e**3*x**4 - 295936*log(x**2)*e**3*x** 3 - 172544*log(x**2)*e**3*x**2 - 49152*log(x**2)*e**3*x - 8192*log(x**2)*e **3 - 18*log(x**2)*x**9 + 1296*log(x**2)*x**8 - 22320*log(x**2)*x**7 - 361 96*log(x**2)*x**6 - 596928*log(x**2)*x**4 - 1661824*log(x**2)*x**3 - 16727 04*log(x**2)*x**2 - 743424*log(x**2)*x - 123904*log(x**2) + 1024*log(x)*e* *9*x**4 - 512*log(x)*e**6*x**5 + 33920*log(x)*e**6*x**4 + 24576*log(x)*e** 6*x**3 + 8192*log(x)*e**6*x**2 + 64*log(x)*e**3*x**6 - 12352*log(x)*e**3*x **5 + 355584*log(x)*e**3*x**4 + 590848*log(x)*e**3*x**3 + 345088*log(x)*e* *3*x**2 + 98304*log(x)*e**3*x + 16384*log(x)*e**3 + 968*log(x)*x**6 - 6...